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A328176 a(n) is the maximal value of the expression d AND (n/d) where d runs through the divisors of n and AND denotes the bitwise AND operator. 3
1, 0, 1, 2, 1, 2, 1, 0, 3, 0, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 3, 2, 1, 4, 5, 0, 1, 4, 1, 4, 1, 0, 3, 0, 5, 6, 1, 2, 1, 0, 1, 6, 1, 2, 3, 2, 1, 4, 7, 0, 1, 4, 1, 2, 1, 4, 3, 0, 1, 4, 1, 2, 1, 8, 5, 2, 1, 2, 3, 4, 1, 8, 1, 0, 5, 2, 3, 4, 1, 8, 9, 0, 1, 6, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..16384

Rémy Sigrist, Scatterplot of the first 2^16 terms

FORMULA

a(n)^2 <= n with equality iff n is a square.

a(n) = 1 for any odd prime number p.

a(n) <= A327987(n).

a(n) = 0 iff n belongs to A327988.

EXAMPLE

For n = 12:

- we have the following values:

    d   12/d  d AND (12/d)

    --  ----  ------------

     1    12             0

     2     6             2

     3     4             0

     4     3             0

     6     2             2

    12     1             0

- hence a(12) = max({0, 2}) = 2.

MAPLE

a:= n-> max(map(d-> Bits[And](d, n/d), numtheory[divisors](n))):

seq(a(n), n=1..100);  # Alois P. Heinz, Oct 09 2019

PROG

(PARI) a(n) = vecmax(apply(d -> bitand(d, n/d), divisors(n)))

CROSSREFS

See A328177 and A328178 for similar sequences.

Cf. A327987, A327988.

Sequence in context: A030205 A159817 A079532 * A191312 A240159 A309447

Adjacent sequences:  A328173 A328174 A328175 * A328177 A328178 A328179

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Oct 06 2019

STATUS

approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)